Is there a stable commensurate solid phase in the second $^{4}$He layer on graphite? -- path integral Monte Carlo study

Existence of a stable commensurate structure in the second $^{4}$He layer on graphite has been a subject of intensive experimental and theoretical studies because of its implication in the possible realization of two-dimensional supersolidity. Earlier path-integral Monte Carlo (PIMC) calculations of Pierce and Manousakis predicted a stable C$_{4/7}$ commensurate structure above the first-layer $^{4}$He atoms fixed at triangular lattice sites [1], but Corboz \textit{et al}. later showed that no commensurate phase was stable when quantum dynamics of the first-layer $^{4}$He atoms was incorporated in the PIMC calculations [2]. On the other hand, recent heat capacity measurements of Nakamura \textit{et al}. provided a strong evidence for a commensurate solid in the second $^{4}$He layer over an extended density range [3]. Motivated by this, we have performed new PIMC calculations for the second helium layer on graphite. Unlike previous PIMC calculations where a laterally-averaged one-dimensional substrate potential was used, we here employ an anisotropic $^{4}$He-graphite potential described by a sum of the $^{4}$He-C pair potentials. With this fully-corrugated substrate potential we make more accurate description of quantum dynamics of the first-layer $^{4}$He atoms and analyze its effects on the phase diagram of the second layer. \\[4pt] [1] M. Pierce and E. Manousakis, \textit{Phys. Rev. Lett.} \textbf{81}, 156 (1998).\\[0pt] [2] P. Corboz \textit{et al}., \textit{Phys. Rev. B} \textbf{78}, 245414 (2008).\\[0pt] [3] S. Nakamura \textit{et al}., arxiv:1406.4388 (2014).